document.write( "Question 171209: Can you PLEASE show me how to graph a quadratic function using its properties?
\n" ); document.write( "p(x)=-x^2+2x-5 Thank You! \n" ); document.write( "

Algebra.Com's Answer #126469 by KnightOwlTutor(293) $\"\"$ $\"About$

You can put this solution on YOUR website!
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Solved by pluggable solver: SOLVE quadratic equation with variable

Quadratic equation $\"ax%5E2%2Bbx%2Bc=0\"$ (in our case $\"-1x%5E2%2B2x%2B-5+=+0\"$ ) has the following solutons:
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\n" ); document.write( " $\"x%5B12%5D+=+%28b%2B-sqrt%28+b%5E2-4ac+%29%29%2F2%5Ca\"$
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\n" ); document.write( " For these solutions to exist, the discriminant $\"b%5E2-4ac\"$ should not be a negative number.
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\n" ); document.write( " First, we need to compute the discriminant $\"b%5E2-4ac\"$ : $\"b%5E2-4ac=%282%29%5E2-4%2A-1%2A-5=-16\"$ .
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\n" ); document.write( " The discriminant -16 is less than zero. That means that there are no solutions among real numbers.

\n" ); document.write( " If you are a student of advanced school algebra and are aware about imaginary numbers, read on.

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\n" ); document.write( " In the field of imaginary numbers, the square root of -16 is + or - $\"sqrt%28+16%29+=+4\"$ .
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\n" ); document.write( " The solution is $\"x%5B12%5D+=+%28-2%2B-+i%2Asqrt%28+-16+%29%29%2F2%5C-1+=++%28-2%2B-+i%2A4%29%2F2%5C-1+\"$
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\n" ); document.write( " Here's your graph:
\n" ); document.write( " $\"graph%28+500%2C+500%2C+-10%2C+10%2C+-20%2C+20%2C+-1%2Ax%5E2%2B2%2Ax%2B-5+%29\"$

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\n" ); document.write( "\n" ); document.write( "Because the squared term is - the parabola is upside down.\r
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